# Question regarding trigonometric composite functions

I have a question from one of my homework sets:

"Let $$f(x)$$ = cos(sin($$3x$$)). Find the smallest positive integer $$k$$ so that $$f(x) = f(x + \pi k).$$"

I know it's simple, but I'm somewhat confused. If someone could just point me in the right direction, it would be greatly appreciated.

Please don't give the answer, just a little help on how I could arrive to the answer.

Thanks!

Hint: \begin{align}f(x+\pi)&=\cos\bigl(\sin(3(x+\pi)\bigr)\\&=\cos\bigl(-\sin(3x)\bigr)\\&=\cos\bigl(\sin(3x)\bigr).\end{align}